Understand the realities of organized crime that helped shape the genre. Real life mobsters often lived lives more astonishing than any movie, and the particular way they did business forms a unique subculture that merits proper study. Don't be content with movie clichés: Research how the Mafia and similar organizations really made their money, the tactics they used and the methods by which they maintained loyalty within their ranks. It will give your screenplay a realism it could never hope to enjoy otherwise.
Examine the structure of the classic mobster story. They typically served as twisted versions of the American dream--the self-made man who used hard work and ingenuity to find success. Classic movie gangsters pursued that goal through brutal and illegal methods, gaining their fondest desires only to see them all come crashing down through the very violence which created them. That tragic arc forms the basis of the mobster genre, and while you should feel free to break from it when writing your screenplay, understanding its basis is absolutely essential.
Consider other forms of organized crime to use as fodder for your screenplay. Classic gangsters were based on Italian and Irish mobsters of the Prohibition era, but think about more modern mobster incarnations, including the Russian mafia, the Asian tongs and the drug cartels of Columbia and Mexico. They each have their subculture and their own way of doing business. Focusing on them might provide your screenplay with a sense of the unique.
Develop a protagonist or series of protagonists to serve as your main characters. They should belong to a given crime syndicate--as underlings, bosses, or even peripheral figures such as lawyers--and the criminal activities they participate in should have a strong bearing on the arc of their character.
Determine the socioeconomic and psychological origins of your mobsters: where they come from, where they're headed and what participation in the mob means for them. From there, you can structure a coherent story charting their rise and fall, or just the means by which their criminal behavior affects otherwise ordinary incidents in their lives. Don't forget to include an antagonist to pit against your mobsters: law enforcement officials, rival gangs or even someone within their organization who thinks things would be better off without them.
Block out the key scenes in your screenplay, noting how your protagonists' criminal activities will affect them. Violence isn't always necessary in mobster screenplays--the threat of it can be enough to convey their dirty business--but a sense of a world operating by different rules should pervade.
Complete a rough draft detailing all of the events you wish to see--the gangster's rise and fall, his ambition and corruption, the things he gains and the cost to his soul along the way.
Polish and revise your rough draft to cut out the dead weight, rendering your mobster story as streamlined as you can make it. Shoot for a running time of two hours (120 pages). Any longer than that and you'll test your audience's patience.